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Finding Pairwise Intersections Inside a Query Range.

ABSTRACT: We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q . We present data structures of size O(n·polylogn) and with query time O((k+1)·polylogn) time, where k is the number of reported pairs, for two classes of objects in R2 : axis-aligned rectangles and objects with small union complexity. For the 3-dimensional case where the objects and the query range are axis-aligned boxes in R3 , we present a data structure of size O(nn·polylogn) and query time O((n+k)·polylogn) . When the objects and query are fat, we obtain O((k+1)·polylogn) query time using O(n·polylogn) storage.

SUBMITTER: de Berg M

PROVIDER: S-EPMC6428404 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Finding Pairwise Intersections Inside a Query Range.

de Berg Mark M Gudmundsson Joachim J Mehrabi Ali D AD

Algorithmica 20171031 11

We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q . We present data structures of size O ( n · polylog n ) and with query time O ( ( k + 1 ) · polylog n ) time, where k is the number of reported pairs, for two classes of objects in R 2 : axis-aligned rectangles and objects with small union complexity. For the 3-dimensional case where ...[more]

PMID: 30956379

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